# Whole genealogies through two row operations

A source row supplies begetting age b and lifespan L; remaining years r=L−b are calculated when not separately attested. Two operations suffice to express any compatible change: R transfers years from remaining life to begetting age, preserving L; A changes remaining life and total lifespan together, preserving b.

| MT to main LXX block | Begetting change | Lifespan change | Preserved quantity |
|---|---:|---:|---|
| Adam, Seth, Enosh, Kenan, Mahalalel, Enoch | +100 | 0 | Lifespan |
| Arphaxad, Shelah | +100 | +27 | Neither component total |
| Eber | +100 | +40 | Neither component total |
| Peleg, Reu, Serug | +100 | +100 | Remaining years |
| Nahor | +50 | +60 | Neither component total |
| Lamech | 0 | −24 | Begetting age |
| Jared, Methuselah, Noah, Shem, Terah | 0 | 0 | Both |

The same century is therefore reused in different ways. Its location and operation matter as much as its size. Five amplitudes—100, −24, 27, 40, 60—with these named supports recover all19 common rows. Combining40 and60 under the additional observed relation40+60=100 gives a four-amplitude description. Both are conditional reconstructions from known source values, not explanations of their historical origin.

Regular chronology accumulates the begetting changes; Cumulative chronology accumulates the lifespan changes. The common-row head differences are1250 and430. Those two totals discard distinctions retained by the full row fields. Native LXX also contains Cainan, adding130 and460, respectively. His numerical equality with Shelah does not supply his name, existence or position.

SP adds two further kinds of connection. Before the Flood, changed begetting ages shorten the capacities to a shared boundary; the cap reduces only lives whose existing margins are exhausted. After the Flood, SP often supplies a concrete intermediate row between MT and LXX. The source thus combines redistribution, lifespan adjustment, clipping and insertion.

The next interface is Rounded chronology. It acts on selected row quantities before accumulation, so it can preserve the common scaffold while obscuring which exact source decomposition produced it.